How much of each ingredients would you need to make 100 quarts of punch

belka [17]

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

$y = (x+25)(x+9)$

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

$y = x^2 + 9x + 25x + 9(25)$

$y = x^2 +34x + 225$

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

$y-225 = x^2 +34x$

$y-225 + 17^2 = x^2 +34x + 17^2$

$y-225 + 289 = (x+17)^2$

$y = (x+17)^2 - 64$

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

<em>x</em> is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

$y=(x+6)(x+6)=(x+6)^2$

Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)

169 = (x+6)^2

Step 3: Solve your equation from Part b for x. (3 points)

$x + 6 = \pm \sqrt{169}$

$x = -6
 \pm 13$

$x= 7 \quad \textrm{ or } \quad x= -19$

Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)

Only the positive root works,

x=7 feet

5 0

3 years ago

Help please ASAPP pleaseee

vagabundo [1.1K]

I think it’s the first option

6 0

2 years ago

PLEASE I REALLY NEED HELP!

vagabundo [1.1K]

Answer:

$\frac{3}{28}$

Step-by-step explanation:

Probability (P) is calculated as

P = $\frac{requiredoutcome}{count}$

The first required outcome is a red sweet from a total of 3 + 5 = 8

P( red) = $\frac{3}{8}$

There are now 2 red left and a count of 7, since 1 has been eaten, thus

P( second red ) = $\frac{2}{7}$

P( red and red ) = $\frac{3}{8}$ × $\frac{2}{7}$ = $\frac{6}{56}$ = $\frac{3}{28}$

6 0

3 years ago

What are the slope and the y-intercept of the linear function that is represented by the graph?

stiv31 [10]

Answer:

uhh the slope is 2/3 but the y-intercepy is -2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (−1, 0).

Hitman42 [59]

<span>The two points that are most distant from (-1,0) are exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3) approximately (0.3333333, 1.885618) and (0.3333333, -1.885618) Rewriting to express Y as a function of X, we get 4x^2 + y^2 = 4 y^2 = 4 - 4x^2 y = +/- sqrt(4 - 4x^2) So that indicates that the range of values for X is -1 to 1. Also the range of values for Y is from -2 to 2. Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis. So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So y = sqrt(4-4x^2) distance is sqrt((x + 1)^2 + sqrt(4-4x^2)^2) =sqrt(x^2 + 2x + 1 + 4 - 4x^2) =sqrt(-3x^2 + 2x + 5) And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving -3x^2 + 2x + 5 Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative. d = -3x^2 + 2x + 5 d' = -6x + 2 And set d' to 0 and solve for x, so 0 = -6x + 2 -2 = -6x 1/3 = x So the furthest point will be where X = 1/3. Calculate those points using (1) above. y = +/- sqrt(4 - 4x^2) y = +/- sqrt(4 - 4(1/3)^2) y = +/- sqrt(4 - 4(1/9)) y = +/- sqrt(4 - 4/9) y = +/- sqrt(3 5/9) y = +/- sqrt(32)/sqrt(9) y = +/- 4sqrt(2)/3 y is approximately +/- 1.885618</span>

7 0

3 years ago